Equilateral Triangle Altitude Calculator
Lightning-fast calculator for equilateral triangle height. Features a 'Type-and-See' interface and vector-perfect rendering.
About
The equilateral triangle is the most symmetrical triangle, where all sides are equal length (a) and all internal angles are 60°. This symmetry creates a fixed ratio between the side length and the altitude.
This tool is optimized for speed. Simply enter the side length, and the altitude is computed instantly using the constant √32.
equilateral
special triangles
Formulas
The height comes directly from the sine of 60°:
h = a sin(60°) = a √32
Reference Data
| Property | Formula | Value (Approx) |
|---|---|---|
| Altitude (h) | a × √32 | 0.866 × a |
| Area (A) | a2 × √34 | 0.433 × a2 |
| Inradius (r) | h3 | 0.289 × a |
Frequently Asked Questions
The square root of 3 is approximately 1.73205. Dividing this by 2 gives 0.866025. This is the ratio of the height to the side length for any equilateral triangle.
No. This specific calculator assumes all three sides are exactly equal. Please use the Isosceles Altitude Calculator for triangles with only two equal sides.